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If given f(x) = x 4 and g(x) = –2x2 3x – 1, what is (f –
g.(x)?
a. (f –
g.(x) = –2x2 4x – 3
b. (f –
g.(x) = –2x2 – 2x 5
c. (f –
g.(x) = 2x2 2x 5
d. (f –
g.(x) = 2x2 – 2x 5

Respuesta :

nobillionaireNobley
f(x) = x + 4
g(x) = -2x^2 + 3x - 1
(f - g)(x) = f(x) - g(x) = x + 4 - (-2x^2 + 3x - 1) = x + 4 + 2x^2 - 3x + 1 = 2x^2 - 2x + 5

Answer:

[tex]2x^2-2x+5[/tex]

Step-by-step explanation:

Given,

[tex]f(x)=x+4[/tex]

[tex]g(x)=-2x^2+3x-1[/tex]

[tex](f-g)(x)=f(x)-g(x)[/tex]        ( Subtraction of two functions )

[tex]=(x+4)-(-2x^2+3x-1)[/tex]  ( By substituting values )

[tex]=x+4+2x^2-3x+1[/tex]      ( Distributive property )

[tex]=2x^2-2x+5[/tex]             ( Combining like terms )

Hence,

[tex](f-g)(x)=2x^2-2x+5[/tex]        

Option d is correct.

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